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A detailed Hamiltonian analysis for a 5D Kalb-Ramond, massive Kalb-Ramond and Stüeckelberg Kalb-Ramond theories with an extra compact dimension is performed. We develop a complete constraint program, then we quantize the theory by constructing the Dirac brackets. From the gauge transformations of the theories, we fix a particular gauge and we find pseudo-Goldstone bosons in Kalb-Ramond and Stüeckelberg Kalb-Ramond systems. Finally we discuss some remarks and prospects. [ABSTRACT FROM AUTHOR]

A pure Dirac's canonical analysis, defined in the full phase space for the Husain-Kuchar (HK) model is discussed in detail. This approach allows us to determine the extended action, the extended Hamiltonian, the complete constraint algebra and the gauge transformations for all variables that occur in the action principle. The complete set of constraints defined on the full phase space allow us to calculate the Dirac algebra structure of the theory and a local weighted measure for the path integral quantization method. Finally, we discuss briefly the necessary mathematical structure to perform the canonical quantization program within the framework of the loop quantum gravity approach. [ABSTRACT FROM AUTHOR]

A pure Dirac's method for Abelian and non-Abelian massive theories in three dimensions is performed. Our analysis is developed on the extended phase space, reporting the relevant structure of the theories, namely, the extended action, the extended Hamiltonian, the full structure of the constraints and the counting of degrees of freedom. In addition, we compare our results with those found in the literature. [ABSTRACT FROM AUTHOR]

We perform Dirac's canonical analysis for a four-dimensional BF and for a generalized four-dimensional BF theory depending on a connection valued in the Lie algebra of SO(3, 1). This analysis is developed by considering the corresponding complete set of variables that define these theories as dynamical, and we find out the relevant symmetries, the constraints, the extended Hamiltonian, the extended action, gauge transformations and the counting of physical degrees of freedom. The results obtained are compared with other approaches found in the literature. [ABSTRACT FROM AUTHOR]

Using a covariant and gauge invariant geometric structure constructed on the Witten covariant phase space for Dirac–Nambu–Goto bosonic p-branes propagating in a curved background, we find the canonically conjugate variables, and the relevant commutation relations are considered. We also find the canonical variables for the Gauss–Bonnet topological term in string theory. [ABSTRACT FROM AUTHOR]

We show that the Witten covariant phase space for p-branes with thickness in an arbitrary background is endowed of a symplectic potential, which although is not important to the dynamics of the system, plays a relevant role on the phase space, allowing us to generate a symplectic structure for the theory and therefore give a covariant description of canonical formalism for quantization. [ABSTRACT FROM AUTHOR]